Use cylindrical coordinates. Evaluate tripleintegral_E sqaureroot x^2 + y^2 dV,
ID: 2878781 • Letter: U
Question
Use cylindrical coordinates. Evaluate tripleintegral_E sqaureroot x^2 + y^2 dV, where E is the region that lies inside the cylinder x^2 + y^2 = 4 and between the planes z = -5 and z = -2. Use cylindrical coordinates. Evaluate tripleintegral_E x^2 dV, where E is the solid that lies within the cylinder x^2 + y^2 = 9, above the plane z = 0, and below the cone z^2 = 16x^2 + 16y^2. Use cylindrical coordinates. Evaluate the integral, where E is enclosed by the paraboloid z = 8 + x^2 + y^2, the cylinder x^2 + y^2 = 4, and the xy-plane. tripleintegral_E e^z dVExplanation / Answer
1)
in cylindrical coordinates
x=rcos, y=rsin
x2+y2=r2
x2+y2=4=22
0<=<=2,0<=r<=2 ,-5<=z<=-2
dv =r dz dr d
E(x2+y2) dv
=[0 to 2] [0 to 2] [-5 to -2] (r2) r dz dr d
=[0 to 2] [0 to 2] [-5 to -2] r2 dz dr d
=[0 to 2] [0 to 2][-5 to -2] r2 z dr d
=[0 to 2] [0 to 2]r2(-2+5) dr d
=[0 to 2] [0 to 2]3r2 dr d
=[0 to 2][0 to 2]r3 d
=[0 to 2] (23 -03)d
=[0 to 2] 8d
=[0 to 2] 8
=8(2-0)
=16
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